Divide ( seventh root of 14x^6)/( seventh root of 2x^5)

$\frac{\sqrt[7]{14 x^{6}}}{\sqrt[7]{2 x^{5}}}$

Combine $\sqrt[7]{14 x^{6}}$ and $\sqrt[7]{2 x^{5}}$ into a single radical.

$\sqrt[7]{\frac{14 x^{6}}{2 x^{5}}}$

Reduce the expression $\frac{14 x^{6}}{2 x^{5}}$ by cancelling the common factors.

Factor $2$ out of $14 x^{6}$ .

$\sqrt[7]{\frac{2 (7 x^{6})}{2 x^{5}}}$

Factor $2$ out of $2 x^{5}$ .

$\sqrt[7]{\frac{2 (7 x^{6})}{2 (x^{5})}}$

Cancel the common factor.

$\sqrt[7]{\frac{2 (7 x^{6})}{2 x^{5}}}$

Rewrite the expression.

$\sqrt[7]{\frac{7 x^{6}}{x^{5}}}$

Cancel the common factor of $x^{6}$ and $x^{5}$ .

Factor $x^{5}$ out of $7 x^{6}$ .

$\sqrt[7]{\frac{x^{5} (7 x)}{x^{5}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[7]{\frac{x^{5} (7 x)}{x^{5} \cdot 1}}$

Cancel the common factor.

$\sqrt[7]{\frac{x^{5} (7 x)}{x^{5} \cdot 1}}$

Rewrite the expression.

$\sqrt[7]{\frac{7 x}{1}}$

Divide $7 x$ by $1$ .

$\sqrt[7]{7 x}$